This K08 project proposal will provide Dr. Caleb Bastian the support necessary to continue training from that of a dental school graduate towards a Ph.D. in Applied and Computational Mathematics (PACM) at Princeton University, with the long-term goal of pursuing an academic career as an independently-funded (NIH R01) biomedical scientist. This proposal is consistent with the NIDCR K08 goal to support dentists who wish to pursue oral health research career development that results in the Ph.D. degree. Also, this K08 project proposal addresses NIDCR strategic aims through development of quantitative approaches in understanding dental and craniofacial disease and focuses on high-throughput data. Princeton University is a research university that has premier mathematics and applied mathematics doctoral programs and world-class high-performance computing resources. Dr. Bastian's training will be under the guidance of mentor Professor Herschel Rabitz and co-mentor Dr. Olga Troyanskaya, both outstanding quantitative scientists, and Dr. Bastian will collaborate with cancer biologist Dr. Hilary Coller at Princeton and consult with system biologist Dr. Doug Darling at the University of Louisville's School of Dentistry. This graduate research project builds upon the didactic and research activities of Dr. Bastian's computational and biological background. In genomics, molecular mechanisms are typically the key regulatory pathways underlying the biological phenomenon (disease, etc), and the growth of high-throughput data has far outpaced the ability to extract reliable regulatory pathways from such data. There is a need for research to address the computational and theoretical aspects analyzing heterogeneous high-throughput and low-throughput data in the context of large calibrated complex integrated multi-scale stochastic biological models. A mathematical statistical inference procedure of this model form would elucidate important interactions across levels and scales and surmise emergent patterns useful to understanding disease pathogenesis. Our hypothesis is that an integrated and calibrated methodology for simultaneous estimation of biological network structure (top-down analysis) and mechanistic model parameters (bottom-up analysis) can be developed to predict molecular regulatory pathways from high-throughput and low-throughput time-course and non-temporal data from diverse biological sources on high-performance computing platforms. Specifically, we intend to: (1) design an integrated methodology that simultaneously estimates and calibrates biological network structure and mechanistic model parameters from biological data, where testing and calibration are accomplished using well-characterized biological systems (Saccharyomyces cerevisiae), and (2) apply the developed calibrated integrated methodology to dental and craniofacial disease data to predicatively generate regulatory networks that represent molecular mechanisms of disruption during disease or major control points in disease pathogenesis. This research project lies at the intersection of top-down and bottom-up analyses, and we will employ techniques from pure and applied mathematics, statistics, and computer science. This quantitative methodology will serve as a biological hypothesis-generating tool. We are particularly interested in studying points of disruption of regulatory networks in OSCC/HNSCC, as phenotypic expression of OSCC/HNSCC is thought to be conditional on an accumulation of genetic defects in a complex, multi-step fashion. This analytical approach has translational relevance, as recent literature has demonstrated that even simple gene expression and pathway analysis can be used to predict survival associated with OSCC-subtypes.